A wire of length L, are of cross section A is hanging from a fixed support. The length of the wire changed to L₁ when mass M is suspended from its free end. The expression for Young's modulus is :

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : ($$\alpha $$_Cu = 1.7 × 10^–5 K^–1 and $$\alpha $$_Al = 2.2 × 10^–5 K^–1)

The unit of thermal conductivity is :

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 $$ \times $$ 10^–2 N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z₀ is :